Question

A map is drawn to a scale of 120 cm to 1 km. How many square cm on the map will represent a hectare of ground?

Answer 1

Hint: The map scale is referring to the relationship or we may say the ratio between the distance on a map and the corresponding distance on real ground. So, we have to compute the area of the portion on the map. Then further it will be converted on real ground. Also, we have to convert the unit in hectares to the unit in a square meter.

Complete step-by-step answer:
First we will convert the units of different kinds given in the question (which are in cm and square cm units).
We know that, 1 km = 1000 m
And, 1 hectare= 10000 square m
Since, 1000 metres will be represented by 120 cm on the Map.
Therefore, it means if we consider the area of a portion, then corresponding conversion will be needed as follows: $1000m \times 1000m$ area will be represented by $120cm \times 120cm$( we consider shape as square).
Means 1000000 square meter will be represented by 14400 square cm on the map.
$\therefore $1 square meter will be represented on the map by,
$\dfrac{{14400}}{{1000000}}$square cm
$\therefore $10000 square meter will be represented on the map by,
$
  \dfrac{{14400}}{{1000000}} \times 10000 \\
   = 144 \\
 $(we have to multiply by 10000)
Thus for 1 hectare ground, 144 square cm map area will be used for representation.

Note: Maps are useful to describe either on large scale or on small scale. Large scale map will show a smaller amount of area with a greater amount of detail. For example, the geographic extent shown on a large scale map will be small. A large-scaled map will be expressed as a representative scale and it will have a smaller number to the right of the ratio.